Is inner product a measurement in quantum computation?

Hams and Raedt gave a quantum computational algorithm to calculate the density of states of a spin system. Starting with an initial random state, they obtain the time evolution of the state. Later they take the inner product of the evolved state with the initial state. How does the inner product formation fit into the quantum computation model? Is it a measurement on the initial and the evolved states?

I have a similar query, wondering whether taking the inner product of two qubits, say phi and psi, <phi|psi> means that the qubits are destroyed afterwards or not. In other words, is it possible to obtain information about their product without being considered as a measurement?